Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,9,2,4}

Atlas Canonical Name {2,6,9,2,4}*1728

Overview

Group
SmallGroup(1728,30790)
Rank
6
Schläfli Type
{2,6,9,2,4}
Vertices, edges, …
2, 6, 27, 9, 4, 4
Order of s0s1s2s3s4s5
36
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

6-fold

9-fold

18-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(26,27)(28,29);;
s2 := ( 3, 6)( 4,12)( 5, 9)( 8,18)(10,13)(11,15)(14,24)(16,19)(17,21)(20,28)(22,25)(23,26)(27,29);;
s3 := ( 3, 4)( 5, 8)( 6,10)( 7, 9)(11,14)(12,16)(13,15)(17,20)(18,22)(19,21)(24,27)(25,26)(28,29);;
s4 := (31,32);;
s5 := (30,31)(32,33);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5*s4*s5*s4*s5, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(33)!(1,2);
s1 := Sym(33)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(26,27)(28,29);
s2 := Sym(33)!( 3, 6)( 4,12)( 5, 9)( 8,18)(10,13)(11,15)(14,24)(16,19)(17,21)(20,28)(22,25)(23,26)(27,29);
s3 := Sym(33)!( 3, 4)( 5, 8)( 6,10)( 7, 9)(11,14)(12,16)(13,15)(17,20)(18,22)(19,21)(24,27)(25,26)(28,29);
s4 := Sym(33)!(31,32);
s5 := Sym(33)!(30,31)(32,33);
poly := sub<Sym(33)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5*s4*s5, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;